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Unfolding an inscribed pyramid

Source: International Olympiad of Metropolises 2019 Problem 5

September 4, 2019
geometry3D geometrypyramidsphereKvant

Problem Statement

We are given a convex four-sided pyramid with apex SS and base face ABCDABCD such that the pyramid has an inscribed sphere (i.e., it contains a sphere which is tangent to each race). By making cuts along the edges SA,SB,SC,SDSA,SB,SC,SD and rotating the faces SAB,SBC,SCD,SDASAB,SBC,SCD,SDA outwards into the plane ABCDABCD, we unfold the pyramid into the polygon AKBLCMDNAKBLCMDN as shown in the figure. Prove that K,L,M,NK,L,M,N are concyclic.
Tibor Bakos and Géza Kós
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